Find records from one table which don't exist in another

There's several different ways of doing this, with varying efficiency, depending on how good your query optimiser is, and the relative size of your two tables:

This is the shortest statement, and may be quickest if your phone book is very short:

SELECT  *
FROM    Call
WHERE   phone_number NOT IN (SELECT phone_number FROM Phone_book)

alternatively (thanks to Alterlife)

SELECT *
FROM   Call
WHERE  NOT EXISTS
  (SELECT *
   FROM   Phone_book
   WHERE  Phone_book.phone_number = Call.phone_number)

or (thanks to WOPR)

SELECT * 
FROM   Call
LEFT OUTER JOIN Phone_Book
  ON (Call.phone_number = Phone_book.phone_number)
  WHERE Phone_book.phone_number IS NULL

(ignoring that, as others have said, it's normally best to select just the columns you want, not '*')

SELECT Call.ID, Call.date, Call.phone_number 
FROM Call 
LEFT OUTER JOIN Phone_Book 
  ON (Call.phone_number=Phone_book.phone_number) 
  WHERE Phone_book.phone_number IS NULL

Should remove the subquery, allowing the query optimiser to work its magic.

Also, avoid "SELECT *" because it can break your code if someone alters the underlying tables or views (and it's inefficient).

The code below would be a bit more efficient than the answers presented above when dealing with larger datasets.

SELECT *
FROM Call
WHERE NOT EXISTS (
    SELECT 'x'
    FROM Phone_book
    WHERE Phone_book.phone_number = Call.phone_number
);

Don't forget to check your indexes!

If your tables are quite large you'll need to make sure the phone book has an index on the phone_number field. With large tables the database will most likely choose to scan both tables.

SELECT *
FROM   Call
WHERE  NOT EXISTS
  (SELECT *
   FROM   Phone_book
   WHERE  Phone_book.phone_number = Call.phone_number)

You should create indexes both Phone_Book and Call containing the phone_number. If performance is becoming an issue try an lean index like this, with only the phone number:

The fewer fields the better since it will have to load it entirely. You'll need an index for both tables.

ALTER TABLE [dbo].Phone_Book ADD CONSTRAINT [IX_Unique_PhoneNumber] UNIQUE NONCLUSTERED 
(
    Phone_Number
)
WITH (STATISTICS_NORECOMPUTE = OFF, IGNORE_DUP_KEY = OFF, ONLINE = ON) ON [PRIMARY]
GO

If you look at the query plan it will look something like this and you can confirm your new index is actually being used. Note this is for SQL Server but should be similar for MySQL.

With the query I showed there's literally no other way for the database to produce a result other than scanning every record in both tables.